Mathematical Practice 1 When presented with a …Attend to precision. Mathematical practice 6 !! I...

Make sense of problems and persevere in solving them. Mathematical Practice 1

When presented with a problem, I can make a plan, carry out my plan, and evaluate its success.

BEFORE…

DURING…

AFTER…

EXPLAIN the problem to myself. � Have I solved a problem like this before? ORGANIZE information… � What is the question? � What do I know? � What do I need to find out? � What tools/strategies will I use?

PERSEVERE

MONITOR my work

ASK myself, “Does this make sense?” CHANGE my plan if it isn’t working out

CHECK � Is my answer correct? � How do my representations connect to my solution?

EVALUATE � What worked/didn’t work? � How was my solution similar or different from my classmates’?

Clip art licensed from the Clip Art Gallery on DiscoverySchool.com Jordan School District 2012, Grade 6

Reason abstractly and quantitatively. Mathematical Practice 2

I can contextualize numbers, decontextualize words, and use reasoning habits to help me make sense of problems.

Contextualize 2.5 x 3 = 7.5

Sam walked 2.5 miles per day for 3 days.

How many total miles did he walk?

Decontextualize

Sam walked 2.5 miles per day for 3 days. How many total miles did he walk?

2.5 x 3 = 7.5

Reasoning Habits

1) Make an understandable representation of the problem.

3) Pay attention to the meaning of the numbers.

2) Think about the units involved. 4) Use the properties of operations or objects.


0 82 3 74 651Miles

08

2 3

7 465

1Days

7.56.55.54.53.52.51.50.5

0 82 3 74 651Miles

08

2 3

7 465

1Days

7.56.55.54.53.52.51.50.5

Construct viable arguments and critique the reasoning of others. Mathematical Practice 3

I can make conjectures and critique the mathematical thinking of others.

I can make, justify (prove), and present arguments by…

• using objects, drawings, diagrams and actions

• using examples and non-examples

• applying context

I can critique the reasoning of others by…

• listening

• asking questions to clarify or improve arguments

• comparing strategies and arguments while identifying flawed logic


Model with mathematics. Mathematical Practice 4

I can recognize math in everyday life and use math I know to solve problems.

I can…

…to solve everyday problems.


April 19, 2012

Use estimates to make the problem

simpler. I will round

to the whole page.

Find importantnumbers.

Pages to read: 247Weeks to read: 2 or 3

Use tools to show relationships.

Weeks to read

Pagesto read

0123

Think about the relationshipto find an answer.

Consider my answer --Does it make sense?

Kylie will need to read 18 pages per day to finish in 2 weeks and 12 pages per day to finish in 3 weeks.

Kylie needs to read a book with 247 pages in 3 weeks. She's hoping to finish it in 2 weeks. About how many pages does she need to read per day?

0361812

The more days Kylie reads, the fewer pages per day she has to read. That makes sense!

Use appropriate tools strategically. Mathematical Practice 5

I can use certain tools to help me explore and deepen my math understanding.

• I know HOW and WHEN to use math tools.

• I can reason: “Did the tool I used give me an answer that makes sense?”


a x b = b x a

V = b x h

-1 0-2-3-4-5 1 2 3 4 5

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Hours

45403025201510

5

-5-10-15-20-25-30-35-40-45

Miles

YX1

2

3

100

200

300

Attend to precision. Mathematical practice 6

I can use precision when solving problems and communicating my ideas.

Mathematicians attend to precision by using…

• math vocabulary with clear definitions

• symbols that have meaning

• context labels

• units of measure

• calculations that are accurate and efficient


May 29, 2012

How much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally?

12

16lb. ÷ 3 people = lb. of chocolate each

units of measure

context

symbols

Look for and make use of structure. Mathematical Practice 7

I can see and understand how numbers and spaces are organized and put together as parts and wholes.

Numbers For Example:

Spaces

For Example:


April 08, 2012

Natural Numbers1, 2, 3…

Whole Numbers0,1, 2, 3...

Integers0, 3, -3….

Rational Numbers2, -3, 1/4, 0, 2.9...

Whole numbers and their opposites

Number that can be expressed as a ratio of two integers

REAL NUMBER SYSTEM

Irrational Numbers√2, , 0.121121112... Real Numbers that cannot be

expressed as a ratio of two integers

\

April 12, 2012

C

Location ~ Distance

The distance from Point A to Point C is 2 units.

A

B

Dimension ~ Nets

V = bh

Measurement ~ Volume

Look for and express regularity in repeated reasoning. Mathematical Practice 8

I can notice when calculations are repeated. Then, I can find more general methods and short cuts.

As I work…

EXAMPLE: I have a container of yogurt that is ¾ full. One serving of yogurt is ¼ of the container. How many servings are left in the container?

(THINK: How many ¼’s are in ¾’s?)

…I think about what I’m trying to figure out while I pay attention to

the details.

I can notice that ¼ is repeated and draw a model to figure out the number of servings

left in the container.

…I evaluate if my results are reasonable.

Once I understand division of fractions, I can use a short cut to solve it like this.

𝟑𝟒 ÷ 𝟏

𝟒 = 𝟑𝟒 x 𝟒𝟏 → 𝟑

𝟒 x 𝟒𝟏 = 𝟏𝟐

𝟒 → 𝟏𝟐

𝟒 = 𝟑𝟏 → 𝟑

𝟏 = 3


April 10, 2012

13/41/21/40Container of Yogurt

1 serving 2 servings 3 servings

Mathematical Practice 1 When presented with a …Attend to precision. Mathematical practice 6 !! I...

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